Quality Analysis of Vinho Verde Wines
Saad Khan
May 01, 2015
- Introduction
- Overview of the Data
- Univariate Plots Section
- Distribution of Alcohol content of wine samples
- pH variation in the dataset
- Sulphate (SO4) distribution of the samples
- Distribution of Sulphur Dioxide (SO2)
- Distribution of Acidic content in the Wine samples
- Sugar content in the Wine samples
- Sugar to acid ratio of Wine samples
- Taste of Wine samples
- Taste of Wine samples due to pH
- Saltiness in Wine samples
- Density of the Wine samples
- Quality of Wine samples
- Univariate Analysis
- What is the structure of your dataset?
- What is/are the main feature(s) of interest in your dataset?
- What other features in the dataset do you think will help support your investigation into your feature(s) of interest?
- Did you create any new variables from existing variables in the dataset?
- Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?
- Bivariate Plots Section
- Correlation between Wine data set variables
- Relation between Quality and Alcohol
- Relationship between Quality and Taste for White wine
- Relationship between Quality and Taste for Red wine
- Alcohol relationship with pH
- Variations in Alcohol with respect to Taste for White wine
- Variations in Alcohol with respect to Taste for Red wine
- Relationship between Quality and Sulphates
- Variations in Quality due to pH for White wine
- Relation between Quality and Citric Acid for Red wine
- Correlation between Density and Residual Sugar for White wine
- Relationship between Density and Fixed Acidity for Red wine
- Bivariate Analysis
- Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?
- Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?
- What was the strongest relationship you found?
- Multivariate Plots Section
- Alcohol with Quality
- Alcohol and Quality with Taste for White wine
- Alcohol and Quality with Taste for Red wine
- pH with Quality
- Relation of Alcohol and pH with Quality for White wine
- Relation of Alcohol and pH with Quality for Red wine
- Sulphates and Quality
- Sulphates and Alcohol with Quality for White wine
- Sulphates and Alcohol with Quality for Red wine
- Residual Sugar with Quality
- Residual Sugar and Alcohol with Quality for White wine
- Residual Sugar and Alcohol with Quality for Red wine
- Acidic Content and Quality
- Acidic Content and Alcohol with Quality
- Chlorides and Quality
- Chlorides and Alcohol with Quality
- Sulphur Dioxide and Quality
- Sulphur Dioxide and Alcohol with Quality
- Density and Quality
- Density and Alcohol with Quality
- Density and Residual Sugar with Quality for White wine
- Density and Fixed Acidity with Quality for Red wine
- Multivariate Analysis
- Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?
- Were there any interesting or surprising interactions between features?
- OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.
- Final Plots and Summary
- Reflection
- References
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Introduction
The task of the project was to analyze the wine data for the Portuguese “Vinho Verde” wine. The data set includes over 10 variables which pertain to the chemical composition of the wines and a resulting categorical variable of quality which is obtained by an average ranking task performed by 3 wine experts. The analysis in this project will attempt to determine the relationship between the chemical contents of wine and its quality rating.
Overview of the Data
Size of the Wine Data Sets
The data set for White wines has more than 4500 entries for 11 variables. Below mentioned are the dimensions of the data set used for this report.
## [1] 4898 18Data set for Red wines has more than 1500 rows with same number of variables as the White wine data set.
## [1] 1599 18NOTE: There are 4 additional variables/features created in order for better representation of data. These will be discussed in the analysis section.
Overview of the Variables
Following are the names of the variables and brief description of the data types for the two data sets. An additional variable was defined in both the data sets to differentiate between the types of wines. This variable will be useful for combined and comparative analysis of the two data sets.
White wine overview
## [1] "X" "fixed.acidity" "volatile.acidity"
## [4] "citric.acid" "residual.sugar" "chlorides"
## [7] "free.sulfur.dioxide" "total.sulfur.dioxide" "density"
## [10] "pH" "sulphates" "alcohol"
## [13] "quality" "type" "combined.acidity"
## [16] "s.a.ratio" "taste" "taste.due.to.pH"## 'data.frame': 4898 obs. of 18 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7 6.3 8.1 7.2 7.2 8.1 6.2 7 6.3 8.1 ...
## $ volatile.acidity : num 0.27 0.3 0.28 0.23 0.23 0.28 0.32 0.27 0.3 0.22 ...
## $ citric.acid : num 0.36 0.34 0.4 0.32 0.32 0.4 0.16 0.36 0.34 0.43 ...
## $ residual.sugar : num 20.7 1.6 6.9 8.5 8.5 6.9 7 20.7 1.6 1.5 ...
## $ chlorides : num 0.045 0.049 0.05 0.058 0.058 0.05 0.045 0.045 0.049 0.044 ...
## $ free.sulfur.dioxide : num 45 14 30 47 47 30 30 45 14 28 ...
## $ total.sulfur.dioxide: num 170 132 97 186 186 97 136 170 132 129 ...
## $ density : num 1.001 0.994 0.995 0.996 0.996 ...
## $ pH : num 3 3.3 3.26 3.19 3.19 3.26 3.18 3 3.3 3.22 ...
## $ sulphates : num 0.45 0.49 0.44 0.4 0.4 0.44 0.47 0.45 0.49 0.45 ...
## $ alcohol : num 8.8 9.5 10.1 9.9 9.9 10.1 9.6 8.8 9.5 11 ...
## $ quality : int 6 6 6 6 6 6 6 6 6 6 ...
## $ type : Ord.factor w/ 1 level "White": 1 1 1 1 1 1 1 1 1 1 ...
## $ combined.acidity : num 7.63 6.94 8.78 7.75 7.75 8.78 6.68 7.63 6.94 8.75 ...
## $ s.a.ratio : num 2.713 0.231 0.786 1.097 1.097 ...
## $ taste : Ord.factor w/ 4 levels "Dry"<"Medium_Dry"<..: 3 1 1 2 2 1 2 3 1 1 ...
## $ taste.due.to.pH : Ord.factor w/ 4 levels "Dry"<"Medium_Dry"<..: 3 2 1 2 2 1 2 3 2 1 ...Red wine overview
## [1] "X" "fixed.acidity" "volatile.acidity"
## [4] "citric.acid" "residual.sugar" "chlorides"
## [7] "free.sulfur.dioxide" "total.sulfur.dioxide" "density"
## [10] "pH" "sulphates" "alcohol"
## [13] "quality" "type" "combined.acidity"
## [16] "s.a.ratio" "taste" "taste.due.to.pH"## 'data.frame': 1599 obs. of 18 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...
## $ type : Ord.factor w/ 1 level "Red": 1 1 1 1 1 1 1 1 1 1 ...
## $ combined.acidity : num 8.1 8.68 8.6 12.04 8.1 ...
## $ s.a.ratio : num 0.235 0.3 0.267 0.158 0.235 ...
## $ taste : Ord.factor w/ 2 levels "Dry"<"Medium_Dry": 1 1 1 1 1 1 1 1 1 1 ...
## $ taste.due.to.pH : Ord.factor w/ 3 levels "Dry"<"Medium_Dry"<..: 3 1 1 1 3 3 2 2 2 2 ...Overview of the Combined Data Set
Combining the two data sets can help us reveal interesting insights to the chemical composition of wines and the resulting variable of quality.
## [1] 6497 18Quality of a Wine Samples (The only categorical variable in the original data)
The quality of a wine samples was rated by at least 3 wine experts and was categorized between ratings from 0 (very bad) and 10 (excellent). In these particular data sets, wine quality ranges between 3 and 9.
## [1] 3 4 5 6 7 8 9Summary of the Data Set
White Wine
## X fixed.acidity volatile.acidity citric.acid
## Min. : 1 Min. : 3.800 Min. :0.0800 Min. :0.0000
## 1st Qu.:1225 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700
## Median :2450 Median : 6.800 Median :0.2600 Median :0.3200
## Mean :2450 Mean : 6.855 Mean :0.2782 Mean :0.3342
## 3rd Qu.:3674 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900
## Max. :4898 Max. :14.200 Max. :1.1000 Max. :1.6600
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 23.00
## Median : 5.200 Median :0.04300 Median : 34.00
## Mean : 6.391 Mean :0.04577 Mean : 35.31
## 3rd Qu.: 9.900 3rd Qu.:0.05000 3rd Qu.: 46.00
## Max. :65.800 Max. :0.34600 Max. :289.00
## total.sulfur.dioxide density pH sulphates
## Min. : 9.0 Min. :0.9871 Min. :2.720 Min. :0.2200
## 1st Qu.:108.0 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100
## Median :134.0 Median :0.9937 Median :3.180 Median :0.4700
## Mean :138.4 Mean :0.9940 Mean :3.188 Mean :0.4898
## 3rd Qu.:167.0 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500
## Max. :440.0 Max. :1.0390 Max. :3.820 Max. :1.0800
## alcohol quality type combined.acidity
## Min. : 8.00 Min. :3.000 White:4898 Min. : 4.130
## 1st Qu.: 9.50 1st Qu.:5.000 1st Qu.: 6.890
## Median :10.40 Median :6.000 Median : 7.405
## Mean :10.51 Mean :5.878 Mean : 7.467
## 3rd Qu.:11.40 3rd Qu.:6.000 3rd Qu.: 7.960
## Max. :14.20 Max. :9.000 Max. :14.960
## s.a.ratio taste taste.due.to.pH
## Min. :0.06459 Dry :3053 Dry :2286
## 1st Qu.:0.23495 Medium_Dry :1591 Medium_Dry :1985
## Median :0.72251 Medium_Sweet: 253 Medium_Sweet: 586
## Mean :0.85776 Sweet : 1 Sweet : 41
## 3rd Qu.:1.28738
## Max. :7.02616Summary: Majority of the white wine samples in this data set have quality around 6 with the mean at 5.9. So we can safely assume that the samples taken were rated by wine experts to have above average quality. The alcohol percentage for most of the samples is around 10-11%. The mean value of total SO2 is around 138 which might cause a slight smell in the nose and taste of wine. The pH of most of the samples is close to 3 which is on the acidic side of the pH scale. The additional variables of combined.acidity and s.a.ratio were created and further used to create categorical variables which helped determine the taste of wine samples. For white wine most fell under the category of dry to medium dry and only a handful of samples were on the sweeter side.
Red Wine
## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00
## Median : 2.200 Median :0.07900 Median :14.00
## Mean : 2.539 Mean :0.08747 Mean :15.87
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00
## Max. :15.500 Max. :0.61100 Max. :72.00
## total.sulfur.dioxide density pH sulphates
## Min. : 6.00 Min. :0.9901 Min. :2.740 Min. :0.3300
## 1st Qu.: 22.00 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500
## Median : 38.00 Median :0.9968 Median :3.310 Median :0.6200
## Mean : 46.47 Mean :0.9967 Mean :3.311 Mean :0.6581
## 3rd Qu.: 62.00 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300
## Max. :289.00 Max. :1.0037 Max. :4.010 Max. :2.0000
## alcohol quality type combined.acidity
## Min. : 8.40 Min. :3.000 Red:1599 Min. : 5.270
## 1st Qu.: 9.50 1st Qu.:5.000 1st Qu.: 7.827
## Median :10.20 Median :6.000 Median : 8.720
## Mean :10.42 Mean :5.636 Mean : 9.118
## 3rd Qu.:11.10 3rd Qu.:6.000 3rd Qu.:10.070
## Max. :14.90 Max. :8.000 Max. :17.045
## s.a.ratio taste taste.due.to.pH
## Min. :0.1053 Dry :1580 Dry :717
## 1st Qu.:0.2117 Medium_Dry: 19 Medium_Dry :691
## Median :0.2482 Medium_Sweet:191
## Mean :0.2854
## 3rd Qu.:0.3008
## Max. :2.0807Summary: Red wine samples in this data set have a median quality of 6 with the mean a little lower at 5.6. So we can safely assume for the samples of this data set as well that they were rated to have above average quality. The alcohol percentage for most of the samples is around 10-10.5%, similar to that of white wine samples. The mean value of total SO2 is around 46.5 which is much lower than what we observed for white wine. The pH of most of the samples is again close to 3. The additional variables created for taste show that red wine samples are mostly on the dry side.
Univariate Plots Section
This section explores the variables in the data set in form of uni-variate charts and plots.
NOTE: For histograms, white bars are used for white wine data and red bars for red wine data.
Distribution of Alcohol content of wine samples
## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect
The alcohol percentage distribution of the wine samples is multimodal with major peak at around 9.5% for both type of wines and smaller peak at 11%. The transformed plot with log10 for alcohol shows a similar distribution as well. The frequency polygon shows that for most of the samples alcohol percentage is between 9% and 13% with multiple peaks.
pH variation in the dataset
## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect
The pH values for the samples seemed to be evenly distribute with mean around 3.2 for white and 3.3 for red wine. The log transformation also shows even distribution of pH. Analysis along with other variables in the bi and multivariate sections might reveal more interesting relationships of pH with other variables in the dataset.
Sulphate (SO4) distribution of the samples
The distribution of sulphates is slightly positively skewed for both wine types while the log transformed plot shows it to be somewhat evenly distributed.
Distribution of Sulphur Dioxide (SO2)
NOTE: To better analyze the histogram below, I have limited the x axis scale to 150 g/dm^3 to avoid the only outlier for white wine at 289 g/dm3. This is evident by the summation performed below.
sum(wqw$free.sulfur.dioxide >150)
## [1] 1Free Sulphur Dioxide
Free sulphur dioxide for white wine samples is evenly distributed while for red wine samples it is positively skewed. Most of the SO2 samples for both wine types are less than 100 mg/dm3. The red wine distribution being heavily skewed, also shows slight bi-modality in the transformed plot.
NOTE: Again, for better analysis x axis scale limit is set to 150 g/dm^3 avoiding 6 outliers for white wine. Summation performed below to double check.
sum(wqw$total.sulfur.dioxide >300)
## [1] 6Total Sulphur Dioxide
Total Sulphur Dioxide being a combination of free and bound SO2 is mostly undetected in wine. Again, the red wine samples are positively skewed while white wine samples show an approximate bell shaped distribution. Skewness for red wine samples shows wide spread with multimodality in the transformed plot just like we saw for Free SO2.
Distribution of Acidic content in the Wine samples
Total Acidic Content
Total acidic content for the two wine types is clearly different. The samples for White wine for all the acid types follow an approximate normal distribution, while the ones for red wine show slight multimodality for fixed.acitdity and multi-modality for volatile.acidity and citric acid.
## [1] 132There are 132 samples of red wine which have no citric acid.
Combined Acidity
The combined acidity plots show a very slight positive skewness for red wine samples while white wine samples follow an approximate normal distribution. This created feature will help determine the taste of the wine samples.
Sugar content in the Wine samples
Histogram for Residual Sugar shows that most of the samples have sugar level between 1-3 g/dm3. The distribution for white wine samples is positively skewed with transformed plot showing multi-modality with peaks at around 0.2, 0.9 and 1.2 g/dm3. On the other hand, the red wine samples seemed to more evenly distributed with slight positive skewness.
Detailed histogram for Residual Sugar also shows that most of the samples have sugar level between 1 - 3 g/dm3. Plot also shows the long tale to the positive side for white wine samples which is in accord with the multi-modality we observed in the transformed plot.
Sugar to acid ratio of Wine samples
The sugar to acid ratio plots are heavily skewed towards the right with the transformed plots showing bi-modality having two significant peaks for white wine samples. While red wine samples are more evenly distributed following an approximate normal distribution. Sugar to acid ratio being a derived variable from residual sugar, shows similar characteristics.
Taste of Wine samples
The overall taste distribution (variable based on the information at this url: http://drinkriesling.com/tastescale/thescale) is on the dry side. Summary for taste variation in both the data sets is shown below.
Taste of White Wine
## Dry Medium_Dry Medium_Sweet Sweet
## 3053 1591 253 1Taste of Red Wine
## Dry Medium_Dry
## 1580 19Taste of Wine samples due to pH
Taste distribution due to pH changes (variable based on the information at this url: http://drinkriesling.com/tastescale/thescale) has been shifted up a bucket to the Medium Dry. Summary for taste variation due to pH in both the data sets is shown below.
Taste of White Wine due to PH
## Dry Medium_Dry Medium_Sweet Sweet
## 2286 1985 586 41Taste of Red Wine due to PH
## Dry Medium_Dry Medium_Sweet
## 717 691 191Saltiness in Wine samples
Plots show most samples for both the types lie between 0-0.1 g/dm3 with few outliers having salt content around 0.4 g/dm3. The transformed plot for white wine samples show peak at -1.25 for white wine samples and -1.2 for the red wine samples.
## X fixed.acidity volatile.acidity citric.acid residual.sugar
## 485 485 6.2 0.370 0.30 6.6
## 1218 1218 8.0 0.610 0.38 12.1
## 4916 18 8.1 0.560 0.28 1.7
## 4918 20 7.9 0.320 0.51 1.8
## 4941 43 7.5 0.490 0.20 2.6
## 4980 82 7.8 0.430 0.70 1.9
## 4982 84 7.3 0.670 0.26 1.8
## 5005 107 7.8 0.410 0.68 1.7
## 5050 152 9.2 0.520 1.00 3.4
## 5068 170 7.5 0.705 0.24 1.8
## 5125 227 8.9 0.590 0.50 2.0
## 5157 259 7.7 0.410 0.76 1.8
## 5180 282 7.7 0.270 0.68 3.5
## 5190 292 11.0 0.200 0.48 2.0
## 5350 452 8.4 0.370 0.53 1.8
## 5591 693 8.6 0.490 0.51 2.0
## 5629 731 9.5 0.550 0.66 2.3
## 5653 755 7.8 0.480 0.68 1.7
## 5950 1052 8.5 0.460 0.59 1.4
## 6064 1166 8.5 0.440 0.50 1.9
## 6159 1261 8.6 0.635 0.68 1.8
## 6218 1320 9.1 0.760 0.68 1.7
## 6269 1371 8.7 0.780 0.51 1.7
## 6271 1373 8.7 0.780 0.51 1.7
## chlorides free.sulfur.dioxide total.sulfur.dioxide density pH
## 485 0.346 79 200 0.99540 3.29
## 1218 0.301 24 220 0.99930 2.94
## 4916 0.368 16 56 0.99680 3.11
## 4918 0.341 17 56 0.99690 3.04
## 4941 0.332 8 14 0.99680 3.21
## 4980 0.464 22 67 0.99740 3.13
## 4982 0.401 16 51 0.99690 3.16
## 5005 0.467 18 69 0.99730 3.08
## 5050 0.610 32 69 0.99960 2.74
## 5068 0.360 15 63 0.99640 3.00
## 5125 0.337 27 81 0.99640 3.04
## 5157 0.611 8 45 0.99680 3.06
## 5180 0.358 5 10 0.99720 3.25
## 5190 0.343 6 18 0.99790 3.30
## 5350 0.413 9 26 0.99790 3.06
## 5591 0.422 16 62 0.99790 3.03
## 5629 0.387 12 37 0.99820 3.17
## 5653 0.415 14 32 0.99656 3.09
## 5950 0.414 16 45 0.99702 3.03
## 6064 0.369 15 38 0.99634 3.01
## 6159 0.403 19 56 0.99632 3.02
## 6218 0.414 18 64 0.99652 2.90
## 6269 0.415 12 66 0.99623 3.00
## 6271 0.415 12 66 0.99623 3.00
## sulphates alcohol quality type combined.acidity s.a.ratio taste
## 485 0.58 9.6 5 White 6.870 0.9606987 Dry
## 1218 0.48 9.2 5 White 8.990 1.3459399 Medium_Dry
## 4916 1.28 9.3 5 Red 8.940 0.1901566 Dry
## 4918 1.08 9.2 6 Red 8.730 0.2061856 Dry
## 4941 0.90 10.5 6 Red 8.190 0.3174603 Dry
## 4980 1.28 9.4 5 Red 8.930 0.2127660 Dry
## 4982 1.14 9.4 5 Red 8.230 0.2187120 Dry
## 5005 1.31 9.3 5 Red 8.890 0.1912261 Dry
## 5050 2.00 9.4 4 Red 10.720 0.3171642 Dry
## 5068 1.59 9.5 5 Red 8.445 0.2131439 Dry
## 5125 1.61 9.5 6 Red 9.990 0.2002002 Dry
## 5157 1.26 9.4 5 Red 8.870 0.2029312 Dry
## 5180 1.08 9.9 7 Red 8.650 0.4046243 Dry
## 5190 0.71 10.5 5 Red 11.680 0.1712329 Dry
## 5350 1.06 9.1 6 Red 9.300 0.1935484 Dry
## 5591 1.17 9.0 5 Red 9.600 0.2083333 Dry
## 5629 0.67 9.6 5 Red 10.710 0.2147526 Dry
## 5653 1.06 9.1 6 Red 8.960 0.1897321 Dry
## 5950 1.34 9.2 5 Red 9.550 0.1465969 Dry
## 6064 1.10 9.4 5 Red 9.440 0.2012712 Dry
## 6159 1.15 9.3 5 Red 9.915 0.1815431 Dry
## 6218 1.33 9.1 6 Red 10.540 0.1612903 Dry
## 6269 1.17 9.2 5 Red 9.990 0.1701702 Dry
## 6271 1.17 9.2 5 Red 9.990 0.1701702 Dry
## taste.due.to.pH
## 485 Dry
## 1218 Medium_Dry
## 4916 Dry
## 4918 Dry
## 4941 Dry
## 4980 Dry
## 4982 Dry
## 5005 Dry
## 5050 Dry
## 5068 Dry
## 5125 Dry
## 5157 Dry
## 5180 Dry
## 5190 Medium_Dry
## 5350 Dry
## 5591 Dry
## 5629 Dry
## 5653 Dry
## 5950 Dry
## 6064 Dry
## 6159 Dry
## 6218 Dry
## 6269 Dry
## 6271 DryHere is a subset of the data set showing outliers for salt content with values greater than 0.3 g/dm3
Detailed plot shows normality in the regular histogram. The major peak is at 0.045 g/dm3 for white wine and at 0.085 g/dm3 for red wine.
Density of the Wine samples
NOTE: Histogram is limited by x axis to view the distribution of density of wine samples with more clarity.
Density for both wine types is primarily observed between 0.98 - 1 gm/cm3 with the distributions following close to normal distribution.
Quality of Wine samples
Quality being the only categorical and the output variable has value of 6 for most of the samples of white wine while 5 is the quality rating given to most of the red wine samples.
Univariate Analysis
What is the structure of your dataset?
The dataset consists of 6497 observations for wines, out of which 4898 are for white wine and the remaining for red wines. In the original data set there were 12 variables with one being an output variable (quality). Quality is based on sensory data provided by at least 3 wine experts and is scored between 0 (poor) and 10 (excellent).
Useful observations at a glance:
- Majority of the wine samples have been rated with quality rating of 6 and mean rating of 5.6
- The mean alcohol content in both type of wines is around 10.5%
- Mean total SO2 for white is 138.4 and red is 46.47, while the max total SO2 are 440 and 289 respectively, suggesting them to be outliers.
- Similar stats can be observed for the free SO2 content in the samples as median values are far below the max values.
- Residual sugar samples for both wine types also show anomalies with max values being extremely high compared to the 3rd quartile values.
What is/are the main feature(s) of interest in your dataset?
Correlation results for Quality and Alcohol are shown below:
White Wine
##
## Pearson's product-moment correlation
##
## data: wqw$alcohol and wqw$quality
## t = 33.8585, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4126015 0.4579941
## sample estimates:
## cor
## 0.4355747Red Wine
##
## Pearson's product-moment correlation
##
## data: wqr$alcohol and wqr$quality
## t = 21.6395, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4373540 0.5132081
## sample estimates:
## cor
## 0.4761663What other features in the dataset do you think will help support your investigation into your feature(s) of interest?
Additional features that might be effective in determining the quality of wine could be pH value, density and sulphate content (which acts as anti-oxidant).
Did you create any new variables from existing variables in the dataset?
The following new variables were created using the existing variables:
- Combination of all the acidity measuring variables were combined to form ‘combined.acidity’, i.e. the sum of fixed.acidity, volatile.acidity & citric.acid. This new variable was used as an input for another new variable.
combined.acidity = fixed.acidity + volatile.acidity + citric.acid
- A variable for ratio of Sugar to Acid (s.a.ratio) in the wine samples was also created to measure the propotion of dryness and sweetness.
s.a.ratio = residual.sugar / combined.acidity
- Taste: Associated with ‘s.a.ratio’ a categorical variable for ‘taste’ was also created to categorize the taste of wine samples as dry, medium dry, medium sweet and sweet. This url: http://drinkriesling.com/tastescale/thescale was used to create the above mentioned ranges for taste. Although, this link provides information for a particular type of wine but I have used it as a way to introduce additional categorical variables. The ranges of ratio for which a wine is categorized by taste might vary in reality for Vinho Verde wines from what I have implemented here in the report.
- Taste due to pH: Based on the ‘taste’ variable and the ‘pH’ value for a particular samples a new variable ‘taste.due.to.pH’ was created to encompass interesting change in taste due to varying pH. Link mentioned above was used to determine the appropriate buckets for taste due to pH.
- A variable for ‘type’ was created when combining the White and Red wine data sets to distinguish between the two.
Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?
The histogram for alcohol when first created showed multi-modality and was hard to interpret. Frequency polygon was created so that the data looks tidier and is easy to interpret. Alcohol being an important feature in the data set, the frequency polygon shows the variations clearly.
Distributions for residual sugar, free sulphur dioxide and sugar to acid ratio were transformed to view modality. Histograms for all of these plots were positively skewed when initially plotted and plotting log10 transformation revealed multi-modality. Plot of residual sugar for white wine samples shows peaks at around 0.2, 0.9 and 1.2. Free sulphur dioxide transformed plot for red wine samples shows multi-modality with no significant peak. The sugar to acid ratio histogram for white wine showed large number of samples with ratio less than 0.25 and when transformed showed multi-modality with peaks at around -0.7, 0.1 and 0.3.
For ease of viewing, some of the plots were adjusted by tweaking the scales. The histograms for chlorides and residual sugar were adjusted by changing scales and binwidth to view the distribution in more detail. Residual sugar content in white wine gave an insight for the widespread distribution of the samples which ultimately was proven by the transformed plot. Adjusting the Chloride plot showed a more sampled version which was easier to interpret.
Bivariate Plots Section
We will start off by tabulating/plotting the original variables from the Wine data sets to infer about interesting relationships.
Correlation between Wine data set variables
Correlation table of White Wine
## Fixed Acid Volatile Acid Citric Acid Sugar Salt Free SO2
## Fixed Acid 1.00 -0.02 0.29 0.09 0.02 -0.05
## Volatile Acid -0.02 1.00 -0.15 0.06 0.07 -0.10
## Citric Acid 0.29 -0.15 1.00 0.09 0.11 0.09
## Sugar 0.09 0.06 0.09 1.00 0.09 0.30
## Salt 0.02 0.07 0.11 0.09 1.00 0.10
## Free SO2 -0.05 -0.10 0.09 0.30 0.10 1.00
## Total SO2 0.09 0.09 0.12 0.40 0.20 0.62
## Density 0.27 0.03 0.15 0.84 0.26 0.29
## pH -0.43 -0.03 -0.16 -0.19 -0.09 0.00
## SO4 -0.02 -0.04 0.06 -0.03 0.02 0.06
## Alcohol -0.12 0.07 -0.08 -0.45 -0.36 -0.25
## Quality -0.11 -0.19 -0.01 -0.10 -0.21 0.01
## Total SO2 Density pH SO4 Alcohol Quality
## Fixed Acid 0.09 0.27 -0.43 -0.02 -0.12 -0.11
## Volatile Acid 0.09 0.03 -0.03 -0.04 0.07 -0.19
## Citric Acid 0.12 0.15 -0.16 0.06 -0.08 -0.01
## Sugar 0.40 0.84 -0.19 -0.03 -0.45 -0.10
## Salt 0.20 0.26 -0.09 0.02 -0.36 -0.21
## Free SO2 0.62 0.29 0.00 0.06 -0.25 0.01
## Total SO2 1.00 0.53 0.00 0.13 -0.45 -0.17
## Density 0.53 1.00 -0.09 0.07 -0.78 -0.31
## pH 0.00 -0.09 1.00 0.16 0.12 0.10
## SO4 0.13 0.07 0.16 1.00 -0.02 0.05
## Alcohol -0.45 -0.78 0.12 -0.02 1.00 0.44
## Quality -0.17 -0.31 0.10 0.05 0.44 1.00Correlation plot of White Wine
## Warning in loop_apply(n, do.ply): Stacking not well defined when ymin != 0## Warning in loop_apply(n, do.ply): Stacking not well defined when ymin != 0## Warning in loop_apply(n, do.ply): Stacking not well defined when ymin != 0## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect
Summary: Density, SO2, sugar, alcohol and acid samples for white wine show correlation with each other. Although poor, density also shows some correlation with salt. Main features for our data set, Alcohol and Quality have a relatively strong correlation of 0.44. Density and sugar have the highest correlation of 0.84. These relationships will be explored in the later sections.
Correlation table of Red Wine
## Fixed Acid Volatile Acid Citric Acid Sugar Salt Free SO2
## Fixed Acid 1.00 -0.26 0.67 0.11 0.09 -0.15
## Volatile Acid -0.26 1.00 -0.55 0.00 0.06 -0.01
## Citric Acid 0.67 -0.55 1.00 0.14 0.20 -0.06
## Sugar 0.11 0.00 0.14 1.00 0.06 0.19
## Salt 0.09 0.06 0.20 0.06 1.00 0.01
## Free SO2 -0.15 -0.01 -0.06 0.19 0.01 1.00
## Total SO2 -0.11 0.08 0.04 0.20 0.05 0.67
## Density 0.67 0.02 0.36 0.36 0.20 -0.02
## pH -0.68 0.23 -0.54 -0.09 -0.27 0.07
## SO4 0.18 -0.26 0.31 0.01 0.37 0.05
## Alcohol -0.06 -0.20 0.11 0.04 -0.22 -0.07
## Quality 0.12 -0.39 0.23 0.01 -0.13 -0.05
## Total SO2 Density pH SO4 Alcohol Quality
## Fixed Acid -0.11 0.67 -0.68 0.18 -0.06 0.12
## Volatile Acid 0.08 0.02 0.23 -0.26 -0.20 -0.39
## Citric Acid 0.04 0.36 -0.54 0.31 0.11 0.23
## Sugar 0.20 0.36 -0.09 0.01 0.04 0.01
## Salt 0.05 0.20 -0.27 0.37 -0.22 -0.13
## Free SO2 0.67 -0.02 0.07 0.05 -0.07 -0.05
## Total SO2 1.00 0.07 -0.07 0.04 -0.21 -0.19
## Density 0.07 1.00 -0.34 0.15 -0.50 -0.17
## pH -0.07 -0.34 1.00 -0.20 0.21 -0.06
## SO4 0.04 0.15 -0.20 1.00 0.09 0.25
## Alcohol -0.21 -0.50 0.21 0.09 1.00 0.48
## Quality -0.19 -0.17 -0.06 0.25 0.48 1.00Correlation plot of Red Wine
## Warning in loop_apply(n, do.ply): Stacking not well defined when ymin != 0## Warning in loop_apply(n, do.ply): Stacking not well defined when ymin != 0## Warning in loop_apply(n, do.ply): position_stack requires constant width:
## output may be incorrect
Summary: For red wine, density, SO2, sugar, salt and acid content samples show stronger correlations with each other. Alcohol and Quality for red wine also have a strong correlation of 0.48. Density and fixed acidity content have the highest correlation with r^2 = 0.67. Relationships are further explored in the sections below.
Now lets explore the relationships in greater detail beginning our analysis with the main variables of interest.
Relation between Quality and Alcohol
Revisiting Alcohol distribution for both types of wines
Scatter Plot for White wine (Quality vs. Alcohol)
Table for Quality vs. Alcohol of White wine
## wqw$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 9.55 10.45 10.34 11.00 12.60
## --------------------------------------------------------
## wqw$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.40 10.10 10.15 10.75 13.50
## --------------------------------------------------------
## wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.000 9.200 9.500 9.809 10.300 13.600
## --------------------------------------------------------
## wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.50 9.60 10.50 10.58 11.40 14.00
## --------------------------------------------------------
## wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.60 10.60 11.40 11.37 12.30 14.20
## --------------------------------------------------------
## wqw$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.50 11.00 12.00 11.64 12.60 14.00
## --------------------------------------------------------
## wqw$quality: 9
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.40 12.40 12.50 12.18 12.70 12.90It is evident that alcohol percentage in the samples tend to produce better quality or the wine expert tend to give higher quality rating to the samples with higher alcohol content. The relationship between alcohol content in the sample seems linear with respect to quality. Summary table and the regression line also shows that quality gets better with increase in mean alcohol content.
Box Plot for White wine (Quality vs. Alcohol)
The box plot reveals another angle to the relationship between quality and alcohol. It turns out that both the mean and median alcohol levels drop from quality rating of 3 to 5. Then for higher rating (above 5) mean and median levels of alcohol increase almost linearly.
Scatter Plot for Red wine (Quality vs. Alcohol)
Table for Quality vs. Alcohol of Red wine
## wqr$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.400 9.725 9.925 9.955 10.580 11.000
## --------------------------------------------------------
## wqr$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.00 9.60 10.00 10.27 11.00 13.10
## --------------------------------------------------------
## wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.5 9.4 9.7 9.9 10.2 14.9
## --------------------------------------------------------
## wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.80 10.50 10.63 11.30 14.00
## --------------------------------------------------------
## wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.20 10.80 11.50 11.47 12.10 14.00
## --------------------------------------------------------
## wqr$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.80 11.32 12.15 12.09 12.88 14.00Red wine data set has fewer observations but shows a positive relation between alcohol and quality. Generally, more the alcohol content better the quality rating. Regression line plotted and the summary table above is also consistent with what is observed in the scatter plot.
Box Plot for Red wine (Quality vs. Alcohol)
Red wine samples show similar trends for alcohol content effect on quality rating. Mean and median alcohol levels fluctuate for lower rating of quality (3-5) and then show gradual increase for higher levels of quality (above 5) maintaining a linear relationship.
Relationship between Quality and Taste for White wine
Plot for Quality vs. Taste of White wine
Plots suggest that most of the samples with higher quality fall under Dry to Medium Dry taste categories. Even though the ranges shift due pH but major contributor towards quality is the sample with taste on the dry side. Summary table for the result is shown below.
Table for Quality vs. Taste of White wine
## wqw$taste: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.958 7.000 9.000
## --------------------------------------------------------
## wqw$taste: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.775 6.000 9.000
## --------------------------------------------------------
## wqw$taste: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.000 5.000 6.000 5.553 6.000 8.000
## --------------------------------------------------------
## wqw$taste: Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6 6 6 6 6 6NOTE: Category Sweet is an exception as it has only one instance.
Table for Quality vs. Taste (pH) of White wine
## wqw$taste.due.to.pH: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.886 6.000 9.000
## --------------------------------------------------------
## wqw$taste.due.to.pH: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.907 6.000 9.000
## --------------------------------------------------------
## wqw$taste.due.to.pH: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.787 6.000 8.000
## --------------------------------------------------------
## wqw$taste.due.to.pH: Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.000 5.000 5.000 5.341 6.000 6.000Relationship between Quality and Taste for Red wine
Plot for Quality vs. Taste of Red wine
For red wine, plots tell a similar story. Samples tend to taste drier than white wine as evident from taste vs. quality histogram (there are no ranges for medium sweet and sweet). Plotting taste due pH changes again show more contribution from the dryer samples towards good quality. Quality for different buckets of taste are summarized below.
Table for Quality vs. Taste of Red wine
## wqr$taste: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.637 6.000 8.000
## --------------------------------------------------------
## wqr$taste: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.000 5.000 6.000 5.526 6.000 6.000Table for Quality vs. Taste (pH) of Red wine
## wqr$taste.due.to.pH: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.681 6.000 8.000
## --------------------------------------------------------
## wqr$taste.due.to.pH: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.618 6.000 8.000
## --------------------------------------------------------
## wqr$taste.due.to.pH: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.534 6.000 8.000Alcohol relationship with pH
Distribution of pH for wine samples revisted
Scatter Plot for White wine (Alcohol vs. pH)
Correlation coefficient for White wine (Alcohol vs. pH)
##
## Pearson's product-moment correlation
##
## data: wqw$alcohol and wqw$pH
## t = 8.5601, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.09374446 0.14893205
## sample estimates:
## cor
## 0.1214321Although, most of the samples of white wine are concentrated in the pH range of 3.0-3.3, there seems to be a slight positive correlation between alcohol and pH. This relationship is shown by the correlation coefficient calculation and the regression line drawn on the scatter plot.
Scatter Plot for Red wine (Alcohol vs. pH)
Correlation coefficient for Red wine (Alcohol vs. pH)
##
## Pearson's product-moment correlation
##
## data: wqr$alcohol and wqr$pH
## t = 8.397, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1582061 0.2521123
## sample estimates:
## cor
## 0.2056325Most of the points are concentrated between pH of 3.2-3.5 and alcohol percentage of 9-11. Apart from the few outliers, there seems to be a positive correlation between the two variables, the factor is confirmed by the correlation test performed. The line of best fit drawn on the scatter plot also confirms a positive relationship between the two variables.
Variations in Alcohol with respect to Taste for White wine
Frequency Plot for Alcohol vs. Taste of White wine
Box Plot for Alcohol vs. Taste of White wine
It is clearly evident from the frequency plots, wine samples that are dry have more alcohol content while sweeter samples have less. Box plots are also consistent with what is in the frequency plots and follow a linear trend showing that decrease in alcohol content leads towards sweeter taste.
Table for Alcohol vs. Taste of White wine
## wqw$taste: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 10.00 10.90 10.94 11.80 14.20
## --------------------------------------------------------
## wqw$taste: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.000 9.100 9.500 9.871 10.400 14.050
## --------------------------------------------------------
## wqw$taste: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.500 8.800 9.100 9.407 9.600 13.000
## --------------------------------------------------------
## wqw$taste: Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 11.7 11.7 11.7 11.7 11.7 11.7NOTE: Category ‘Sweet’ in taste vs. alcohol is an exception as it has only one instance.
Table for Alcohol vs. Taste (pH) of White wine
## wqw$taste.due.to.pH: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.90 10.80 10.89 11.89 14.20
## --------------------------------------------------------
## wqw$taste.due.to.pH: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 9.30 10.00 10.26 11.00 14.05
## --------------------------------------------------------
## wqw$taste.due.to.pH: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.000 9.100 9.800 9.981 10.500 14.000
## --------------------------------------------------------
## wqw$taste.due.to.pH: Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.700 8.800 9.500 9.622 10.100 12.400Variations in Alcohol with respect to Taste for Red wine
Frequency Plot for Alcohol vs. Taste of Red wine
Box Plot for Alcohol vs. Taste of Red wine
For red Wine, plot colored by taste does not depict the exact effect of alcohol on taste as samples with ‘Medium Dry’ range are pretty low. Plotting alcohol colored by taste.due.to.pH reveals a linear trend showing that with increase in alcohol percentage, taste gets sweeter.
Table for Alcohol vs. Taste of Red wine
## wqr$taste: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.20 10.43 11.10 14.90
## --------------------------------------------------------
## wqr$taste: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.800 9.200 9.900 9.984 10.400 12.200Table for Alcohol vs. Taste (pH) of Red wine
## wqr$taste.due.to.pH: Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.00 10.29 11.00 14.90
## --------------------------------------------------------
## wqr$taste.due.to.pH: Medium_Dry
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.70 9.50 10.30 10.41 11.00 14.00
## --------------------------------------------------------
## wqr$taste.due.to.pH: Medium_Sweet
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.233 9.850 10.800 10.960 11.700 14.000Relationship between Quality and Sulphates
Sulphates revisited
Scatter Plot for White wine (Quality vs. Sulphates)
Box Plot for White wine (Quality vs. Sulphates)
Table and Correlation Coefficient for Quality vs. Sulphates of White wine
## wqw$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2800 0.3800 0.4400 0.4745 0.5425 0.7400
## --------------------------------------------------------
## wqw$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2500 0.3800 0.4700 0.4761 0.5400 0.8700
## --------------------------------------------------------
## wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2700 0.4200 0.4700 0.4822 0.5300 0.8800
## --------------------------------------------------------
## wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2300 0.4100 0.4800 0.4911 0.5500 1.0600
## --------------------------------------------------------
## wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2200 0.4100 0.4800 0.5031 0.5800 1.0800
## --------------------------------------------------------
## wqw$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2500 0.3800 0.4600 0.4862 0.5850 0.9500
## --------------------------------------------------------
## wqw$quality: 9
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.360 0.420 0.460 0.466 0.480 0.610##
## Pearson's product-moment correlation
##
## data: wqw$sulphates and wqw$quality
## t = 3.7613, df = 4896, p-value = 0.000171
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02571007 0.08156172
## sample estimates:
## cor
## 0.05367788The Sulphates relation with quality of white wine shows no significant correlation. For mean sulphate content it shows fluctuating trend between rating 3-5, then increases very slightly from rating 5-7 followed by a drop for rating 8 and 9 as observed in the box plot representation. The median value of sulphate content (as per the summary table) for all quality buckets is almost the same i.e. (0.46-0.48). This observation is also confirmed by the low correlation coefficient value and the regression line drawn, which is almost parallel to the x axis.
Scatter Plot for Red wine (Quality vs. Sulphates)
Box Plot for Red wine (Quality vs. Sulphates)
Table and Correlation Coefficient for Quality vs. Sulphates of Red wine
## wqr$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4000 0.5125 0.5450 0.5700 0.6150 0.8600
## --------------------------------------------------------
## wqr$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.4900 0.5600 0.5964 0.6000 2.0000
## --------------------------------------------------------
## wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.370 0.530 0.580 0.621 0.660 1.980
## --------------------------------------------------------
## wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4000 0.5800 0.6400 0.6753 0.7500 1.9500
## --------------------------------------------------------
## wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3900 0.6500 0.7400 0.7413 0.8300 1.3600
## --------------------------------------------------------
## wqr$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.6300 0.6900 0.7400 0.7678 0.8200 1.1000##
## Pearson's product-moment correlation
##
## data: wqr$sulphates and wqr$quality
## t = 10.3798, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2049011 0.2967610
## sample estimates:
## cor
## 0.2513971Red wine samples have a slightly better correlation between sulphates and quality compared to white wine. As evident from the box plots, regression line and the scatter plot, increase in sulphates per samples on average results in a better quality rating. This is also evident in the summary table, mean and median values for sulphate content show increasing trend and so does the correlation coefficient .
Variations in Quality due to pH for White wine
Scatter Plot for White wine (Quality vs. pH)
Box Plot for White wine (Quality vs. pH)
Table and Correlation Coefficient for Quality vs. pH of White wine
## wqw$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.870 3.035 3.215 3.188 3.325 3.550
## --------------------------------------------------------
## wqw$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.830 3.070 3.160 3.183 3.280 3.720
## --------------------------------------------------------
## wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.790 3.080 3.160 3.169 3.240 3.790
## --------------------------------------------------------
## wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.720 3.080 3.180 3.189 3.280 3.810
## --------------------------------------------------------
## wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.840 3.100 3.200 3.214 3.320 3.820
## --------------------------------------------------------
## wqw$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.940 3.120 3.230 3.219 3.330 3.590
## --------------------------------------------------------
## wqw$quality: 9
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.200 3.280 3.280 3.308 3.370 3.410##
## Pearson's product-moment correlation
##
## data: wqw$pH and wqw$quality
## t = 6.9917, df = 4896, p-value = 3.081e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07162022 0.12707983
## sample estimates:
## cor
## 0.09942725The relationship between quality and pH shows a slight linear trend. Mean and median values (as viewed in the box plot and summary table) for pH decrease slightly for lower quality ratings between 3-5 and then start to gradually increase showing slight contribution towards the quality of the white wine samples. The overall slight positive trend is also depicted by the regression line accompanying the scatter plot and the r^2 value.
Relation between Quality and Citric Acid for Red wine
Citric Acid Histogram for Red wine samples
Scatter Plot for Red wine (Quality vs. Citric Acid)
Box Plot for Red wine (Quality vs. Citric Acid)
Table and Correlation Coefficient for Quality vs. Citric Acid of Red wine
## wqr$quality: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0050 0.0350 0.1710 0.3275 0.6600
## --------------------------------------------------------
## wqr$quality: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0300 0.0900 0.1742 0.2700 1.0000
## --------------------------------------------------------
## wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0900 0.2300 0.2437 0.3600 0.7900
## --------------------------------------------------------
## wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0900 0.2600 0.2738 0.4300 0.7800
## --------------------------------------------------------
## wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.3050 0.4000 0.3752 0.4900 0.7600
## --------------------------------------------------------
## wqr$quality: 8
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0300 0.3025 0.4200 0.3911 0.5300 0.7200##
## Pearson's product-moment correlation
##
## data: wqr$citric.acid and wqr$quality
## t = 9.2875, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1793415 0.2723711
## sample estimates:
## cor
## 0.2263725The scatter plot, regression line and mean-median values on box plot for citric acid show gradual increase with increase in quality or it can be said, quality increases as citric acid content increases for the samples of Red wine. This is also depicted by the calculated r^2 value.
Let us explore interesting correlations between features other than the main features, i.e. alcohol and quality.
Correlation between Density and Residual Sugar for White wine
NOTE: I chose the variables that had the strongest correlation, i.e density and residual sugar for white wine and density and fixed acidity for red wine.
Scatter Plot for White wine (Density vs. Residual Sugar)
NOTE: In the scatter plot below, scales are limited to exclude outliers.
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## values (geom_path).
Correlation coefficient for White wine (Density vs. Residual Sugar)
##
## Pearson's product-moment correlation
##
## data: wqw$density and wqw$residual.sugar
## t = 107.8749, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8304732 0.8470698
## sample estimates:
## cor
## 0.8389665The scatter plot and correlation coefficient clearly show a strong relation between density and residual sugar for white wine samples. An r^2 of 0.84 suggests that density and residual sugar can be associated in form of a linear equation which is confirmed by the regression line.
Relationship between Density and Fixed Acidity for Red wine
Scatter Plot for Red wine (Density vs. Fixed Acidity)
Correlation coefficient for Red wine (Density vs. Fixed Acidity)
##
## Pearson's product-moment correlation
##
## data: wqr$density and wqr$fixed.acidity
## t = 35.8771, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6399847 0.6943302
## sample estimates:
## cor
## 0.6680473The scatter plot for red wine data has wide distribution of points but shows very high correlation between density and fixed acidity. This is also evident from the regression line plot and the correlation coefficient calculation above.
Bivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?
Relationships observed in this section are as follows:
Quality with Alcohol: Scatter plots, regression line and box plots were created to identify this relation. Quality and Alcohol being the main features in the data sets, for both White and Red wines, showed high correlation of 0.44 and 0.48 respectively. Scatter plots and regression line helped view the bigger picture, i.e. positive correlation between Quality and Alcohol while box plots showed more depth, showing for lower quality ratings (3-5) alcohol levels drop and then gradually increase linearly after quality level 5.
Quality with Taste and Taste due to pH: New categorical variables of Taste and Taste due to pH were created to view how taste of wine samples effected the quality. The ranges and names for taste were set according to the link mentioned in the ‘Univariate’ section. Histograms of quality were plotted, for both white and red wine samples, with color set as ‘taste’ and ‘taste due to pH’. For White wine, the major taste contributors towards higher quality were the ‘dry’ to ‘medium dry’ tasting samples. There was an exception in case of the only ‘sweet’ tasting sample for white wine. Red wine samples showed similar characteristics, i.e. more dry the taste of the sample, better the quality rating given to them.
Alcohol relationship with pH: For white wine, samples were concentrated in the pH range of 3.0-3.3 and mostly under alcohol percentage of 10.5. Lot of scattering made it difficult to identify the extent of correlation between the two variables so the scatter plot was accompanied by a regression line and r^2 was calculated, the outcome came to low but positive showing some relation. For red wine, most of the points were observed to be concentrated between pH of 3.2-3.5 and alcohol percentage of 9-11. By looking at the scatter plot, visually there seemed to be reasonable correlation between these variable which was confirmed by the regression line and the calculated r^2 of 0.2.
Alcohol with respect to Taste and Taste due to pH: White wine samples that taste on the dry side tend to have more alcohol content while sweeter tasting samples have less alcohol. For red wine, samples that are dry have lesser alcohol content compared to the sweeter ones. This observation is evident by the box plot representation in the Bivariate Plots section.
Quality vs. Sulphates: Box plots, scatter plots and regression line were created to determine the relation between quality and sulphates. It seemed that white wine samples had poor correlation compared to red wine samples, confirmed by the r^2 calculated. For white wine, sulphate content slightly increased from quality rating of 3-7 and then dropped from then on. On the other hand, samples for red wine had better correlation as increase in average sulphate content per sample showed increase in quality.
Quality with pH for White wine: Relation of quality and pH for white wine samples followed a parabolic function, i.e. when mean and median values of pH are plotted for each quality rating bucket, the pH value decreased till the quality rating of 5(minima) and then started to gradually increase. The iverall positive trend was also depicted by the R^2 value calculated.
Quality with Citric Acid for Red wine: Scatter plot and the regression line showed close to a linear relationship between quality and citric acid for samples of red wine. Box plots and the r^2 value further made it clear that quality generally increases as citric acid content on average increase per sample of red wine.
Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?
There were interesting correlations observed between other features in the two data sets. The features showing highest correlation coefficient for each of the wine type were chosen:
Correlation between Density and Residual Sugar for White wine: Scatter diagram and regression line were plotted and correlation coefficient was calculated to view the relation between density and residual sugar for white wine. The correlation was observed to be very strong (r^2 = 0.84).
Relationship between Density and Fixed Acidity for Red wine: Again, density and fixed acidity were plotted against each other using scatter plot and regression line functionality. Most of the points were observed to be in the range of density of 0.99 - 1.00 g/cm^3 for red wine. Along with the plots, correlation coefficient was also computed between density and fixed acidity which showed a stronger correlation for the red wine samples (r^2 = 0.67).
What was the strongest relationship you found?
The strongest relationship observed was between density and residual sugar for white wine samples (r^2 = 0.84)
Other notable correlations are as follows:
- Density vs. Fixed Acidity for red wine (r^2 = 0.67)
- Quality with Alcohol for both data sets (r^2 = 0.48[Red] and r^2 = 0.44[White])
Multivariate Plots Section
This section covers exploring relationships between multiple variables of the two wine data sets. Let us start with the main features first.
Alcohol with Quality
Density Plot of Alcohol with Quality for White wine
The density plot shows us clearly, samples with lower percentage of alcohol content lead the wine experts to give lower ratings and increase in alcohol content specially greater than 11% (with and exception in quality rating 9) generally leads them to give higher ratings like 6, 7, 8 or 9.
Density Plot of Alcohol with Quality for Red wine
The density plot for red wine shows a similar trend. Lower the percentage of alcohol, lower the rating given to the sample and vice versa.
Let us introduce another variable and look for more interesting patterns.
Alcohol and Quality with Taste for White wine
Box Plot for White wine (Quality vs. Alcohol) with Taste
Facet wrapping by taste does show an overall positive relationship between quality and alcohol. For ‘Dry’ tasting samples alcohol content decreases between ratings 3-5 and almost linearly increases for ratings 5 and above. ‘Medium Dry’ taste bucket shows a similar trend as the ‘Dry’ bucket with the exception of rating 9. There are fewer samples in the ‘Medium Sweet’ bucket compared to the other two but the trend observed is positive. Taste bucket for ‘Sweet’ is an exception as there was only one sample which tasted sweet.
Box Plot for White wine (Quality vs. Alcohol) with Taste due to pH
Bringing pH into the equation, show similar results which was as expected. Again with the exception of the ‘Sweet’ taste bucket, rest of the buckets show fluctuation but overall decrease in alcohol content between lower quality ratings 3-5 and then linear increase from quality rating 5 onwards.
Alcohol and Quality with Taste for Red wine
Box Plot for Red wine (Quality vs. Alcohol) with Taste
As the samples for the red wine data sets are less compared to white wine, plotting alcohol vs. quality with taste does not tell us much. The ‘Dry’ bucket shows fluctuating trend for alcohol from rating 3-5 and linear increase for higher quality rating values. Below is a plot using taste due to pH.
Box Plot for Red wine (Quality vs. Alcohol) with Taste due to pH
Shifting to pH, we only have three taste buckets. For ‘Dry’ taste we see a linear positive trend, i.e. increase in alcohol content improves the quality rating. For ‘Medium Dry’ and ‘Medium Sweet’, alcohol content fluctuates slightly for lower quality ratings and then starts to increase as the quality rating gets better.
pH with Quality
Density Plot of pH with Quality for White wine
Plotting pH shows that (apart from the exception of quality rating 3 where pH covers a wide-range) most of the mid-range quality ratings are given to samples with pH from 3.0-3.2. Looking at quality rating 8 and 9 we see that there is slight increase in pH range which tells us that pH plays a role in the higher rated samples of white wine.
Density Plot of pH with Quality for Red wine
In contrast to white wine, higher ranges of pH per sample for red wine tend to receive poor ratings (the shift in the lower rating curves towards higher pH) and vice versa.
Relation of Alcohol and pH with Quality for White wine
Scatter Plot for White wine (Alcohol vs. pH) with Quality
Again, to analyze the trend here I have only selected the quality rating bucket with most samples. It can be seen for samples with lower percentage of alcohol and slightly higher pH the quality tends to suffer. On the other hand, for samples with higher alcohol content (greater than 11%) and a stable pH (eg: 3.2) the experts give good quality rating.
Relation of Alcohol and pH with Quality for Red wine
Scatter Plot for Red wine (Alcohol vs. pH) with Quality
Applying the same quality bucket configuration to red wine samples reveals similar results. With less alcohol content and pH on a higher side, experts tend to give lower ratings. In contrast to this for more alcohol content and pH controlled under 3.3 leads the expert to rank the samples high.
Sulphates and Quality
Density Plot of Sulphates with Quality for White wine
For white wine, sulphate content seems not to effect the quality rating that much. The exception is the curve for rating 9 with a spike close to 0.6 g/dm3 apart from that most of the curves for quality rating buckets overlap with each other.
Density Plot of Sulphates with Quality for Red wine
Here things look different from white wine samples. Red wine samples that receive high quality rating do have access of sulphates in them as can be seen from the curves for rating 7 and 8. There peaks stand out alone from the rest at sulphate content of 0.7 g/dm3 or more.
Sulphates and Alcohol with Quality for White wine
Scatter Plot for White wine (Sulphates vs. Alcohol) with Quality
The plot for alcohol and sulphates shows samples binned by quality rating. It is difficult to find a trend with a number of outliers over the edges. Lets look at the zoomed version in the plot below.
Scatter Plot for White wine (Sulphates vs. Alcohol) with Quality [zoomed]
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## values (geom_point).
I filtered the quality buckets and can only view from quality rating 5-7 (majority of the points). The points plotted are mostly scattered and do not give a very good trend as to how sulphates effect quality (in accordance with the density plots in the section above).
Sulphates and Alcohol with Quality for Red wine
Scatter Plot for Red wine (Sulphates vs. Alcohol) with Quality
NOTE: Axes scaled to avoid outliers and better represent the data.
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## (geom_point).
Scatter plot for red wine samples is pretty straight forward and shows some degree of linearity between alcohol and sulphate content. Higher alcohol percentage and more sulphate content (around 0.8-1.0 g/dm3) leads to higher quality rating (greater than 6). The lower quality ratings (3-5) mostly occur in the region where we have low sulphate content and low alcohol percentage.
Residual Sugar with Quality
Density Plot of Residual Sugar with Quality for White wine
In my opinion, residual sugar plays an important part for the expert to decide the quality rank for a particular wine sample. By looking at the plot it looks like most of high rated samples have less than 5 g/dm3. For the remaining samples, quality ratings fluctuate between residual sugar range of 10-20 g/dm3.
Density Plot of Residual Sugar with Quality for Red wine
Most of the samples, independent of the quality rating hey receive have residual sugar level less than 4 g/dm3. For samples with residual sugar more than 4 g/dm3, ratings are mixed, i.e. not following a certain pattern.
Residual Sugar and Alcohol with Quality for White wine
Scatter Plot for White wine (Residual Sugar vs. Alcohol) with Quality
NOTE: Few outliers were excluded for better anaylsis of the data.
## Warning in loop_apply(n, do.ply): Removed 5 rows containing missing values
## (geom_point).
Most of the points in the scatter plot are concentrated at less than 5 g/dm3 of residual sugar as seen in the density plot and it can be viewed here in the scatter plot that samples with more sugar content do receive higher quality ratings.
Residual Sugar and Alcohol with Quality for Red wine
Scatter Plot for Red wine (Residual Sugar vs. Alcohol) with Quality [zoomed]
## Warning in loop_apply(n, do.ply): Removed 129 rows containing missing
## values (geom_point).
The zoomed version of scatter for red wine does show a trend. Samples that get higher quality ratings have residual sugar under 2.5 g/dm3 and alcohol content more than 11%. Samples with mid-range quality ratings (5-6) have more residual sugar content and alcohol percentage less 10% on average.
Acidic Content and Quality
Total Acidic Content with Quality (White wine on left and Red wine on right)
Fixed and Volatile Acidity: Red and white wine both have similar trends, samples with higher ratings tend to have fixed and volatile acidic content between 6-9 g/dm3 and 0.3-0.4 g/dm3 respectively, while lower ratings have fixed and volatile acidic content varying over a wide range.
Citric Acid: For white wine, almost all of the samples have citric acid content less than 0-0.6 g/dm3 and quality ratings vary between this bracket. For red wine, all samples have citric acid less than 1 g/dm3 where samples with high quality ratings have acid content more than 0.3 g/dm3 while the one with lower ratings have citric acid content less than 0.25 g/dm3 as seen in the density plot..
Acidic Content and Alcohol with Quality
Scatter plot for Total Acidic Content and Alcohol with Quality (White wine on left and Red wine on right)
NOTE: Outliers from all the acidic content plots were carefully observed and excluded for better analysis.
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## values (geom_point).
White wine: General trend seems that increase in acidic content does not play an important part in improving quality, however, it can be seen that samples with increase in volatile acidity do get lower ratings.
Red wine: There is a definite trend here, samples with increased alcohol percentage and increased form of any acidic content tends to get higher quality rating and vice versa (specially fixed acidity and citric acid).
Chlorides and Quality
Density Plot of Chlorides with Quality for White wine
Salts in drinks should be balanced. It can be observed in the plot that white wine samples with salts more than 0.05g/dm3 get mid-range to lower-range quality rating from the experts, while balanced samples get better ratings (7-9). A samples(s) can be seen clearly receiving lowest rating of 3 as the salt content seems to be sky rocketing (around 0.24 g/dm3)
Density Plot of Chlorides with Quality for Red wine
Most of the samples have chlorides levels under 0.1 g/dm3 and quality is almost independent as rating curves overlap with each other. Again curve for rating 3 shows variations showing that there were samples that were excessively salty.
Chlorides and Alcohol with Quality
Scatter Plot for (Chlorides vs. Alcohol) with Quality [Facet Wrap]
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## (geom_point).
I tried a different approach here, used the combination of the two data sets. It can be seen, chloride amount under controllable levels (i.e. less than 0.15 g/dm3) has never effected the quality. It is only when saltiness increases we see samples start to get lower values of rating for both the wine types.
Sulphur Dioxide and Quality
SO2 with Quality (White wine on left and Red wine on right)
Most of the samples that get good quality ratings for white wine contain total SO2 in the range of 0-150 g/dm3 and Free SO2 in the range of 25-50 g/dm3. There are samples that have more SO2 content and ultimately get poor ratings from the experts. On the other hand, majority of the red wine samples that get higher rating have much lower amount of SO2. Looking at the ratings, it seems that ideal range of SO2 for red wine is less than 50 g/dm3 for total and less than 20 g/dm3 for free SO2.
Sulphur Dioxide and Alcohol with Quality
Scatter plot for Total Sulphur Dioxide and Alcohol with Qualtiy (White wine on left and Red wine on right)
NOTE: Again, outliers for SO2 content plots are excluded for better analysis.
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## (geom_point).
White wine: There does not seem to be a very good relation between the variables but to some extent samples with increase of alcohol and controlled amount of total and free SO2 tend to get higher ratings.
Red wine: Here it looks like there is very good relationship between the 3 variables. Specially for free SO2, it can clearly be observed that increase in both alcohol and free SO2 leads the experts give higher ratings.
Density and Quality
Density Plot of Density with Quality for White wine
Samples that have density controlled and close to 0.99 g/cm3 tend to high quality rating. Ratings starts to decrease as value of density increases and starts to approach 1.00 g/cm3.
Density Plot of Density with Quality for Red wine
Again for red wine also, most samples that have density close to and less than 0.995 g/cm3 get a higher rating. And as we go towards higher density, experts think the samples loosing and the wow factor and they give lower ratings.
Density and Alcohol with Quality
Scatter Plot for (Density vs. Alcohol) with Quality [Facet Wrap]
NOTE: Few density outliers removed from the plots for better representation.
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## (geom_point).
Again, facet wrapping was used to identify trends in different quality buckets. In general, there does not seem to be any trends between density and quality with introduction of alcohol.
In the end, let us observe trends of quality for the variables with the highest correlation.
Density and Residual Sugar with Quality for White wine
Scatter Plot for (Density vs. Residual Sugar) with Quality
NOTE: Scatter plot modified to exclude outliers for ease of visual representation.
## Warning in loop_apply(n, do.ply): Removed 5 rows containing missing values
## (geom_point).
Density and residual sugar for white wine have the highest correlation and it can be seen here in the plot. Adding a line for reference, a divide can be seen. For increasing residual sugar per sample if the density remains in levels below the imaginary line, samples get high ratings (7-9) and if it shoots up the threshold set by the line, the quality starts to suffer.
Density and Fixed Acidity with Quality for Red wine
Scatter Plot for (Density vs. Fixed Acidity) with Quality
Both the variables having very good correlation, do show a definite trend for quality. On average the samples with higher fixed acidic content (more than 8 g/dm3) and density of less than or equal to 0.996 /cm3 receive higher quality ratings. As the fixed acidity starts to go below 8 g/dm3 and density approaches 1.00 g/dm3 samples start to receive poor to mid range ratings.
Multivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?
Relationships explored in the multivariate section are as follows:
Alcohol and Quality with Taste: Density and scatter plots were used to explore the relationship between these features. For both the wine types, density plots showed that with increase in percentage of alcohol there was an increase in the quality rating for the samples. Taste due to pH was the additional variable added to the equation and it was observed that for white wine samples, with increase in alcohol they started to taste in the ‘Dry’ to ‘Medium Dry’ range and ultimately quality rating increased. On the other hand, for red wine, with introduction of taste due to pH there was not much of trend or a relation seen between these variables.
NOTE: Here samples for white wine in particular strengthen each other in terms of the variables alcohol, taste and quality.
Relation of Alcohol and pH with Quality: In general, according to the density plot for white wine, mid to low range quality rating did not really depend upon pH while for increasing pH there was improvement seen the ratings specially (8 and 9). Red wine samples told a different story, higher the pH value of the samples, lower the rating it got by the experts and vice versa. Scatter plots showed similar results for both wine types. Samples with lesser amount of alcohol and pH on the higher side tend to receive poor ratings while samples with alcohol greater than 11% and stable pH of around 3.2-3.3 received high ratings.
NOTE: I think pH, alcohol and quality strengthened each other for white wine samples.
Alcohol and Quality and Sulphates: For white wine samples, on average sulphate content did not effect the quality rating as such, however, red wine samples did show a trend. Samples with sulphate content around 0.7 g/dm3 received higher ratings compared to the ones with sulphates around 0.5 g/dm3. For scatter plots of white wine with alcohol, quality and sulphates it was difficult to pin point a particular trend. For red wine, there was a definite positive trend, i.e. higher the alcohol and sulphate content per sample, higher the ratings they got from wine experts.
NOTE: Sulphate and alcohol played a part in improving the quality rating, hence strengthening each other in case of red wine samples.
Relationship of Residual Sugar and Alcohol with Quality: The density plots for residual sugar with curves colored by quality rating did not really show a clear trend. Most of the quality curves are stacked in the same ranges of residual sugar for both the wine types. The scatter plot for white wine did show a relation between the variables, i.e. samples with more residual sugar did receive higher ratings. The zoomed version of scatter plot for red wine samples showed that for higher ratings, the alcohol content was observed be higher and residual sugar content was observed to be lower and vice versa.
NOTE: In my opinion, variables residual sugar, quality and alcohol do strengthen each other to some extent for samples of red wine.
Were there any interesting or surprising interactions between features?
Density and Residual Sugar with Quality for White wine: Density and residual sugar for white wine showed the highest correlation with each other. I thought of investigating the trend of these two variables with our main variable of interest. I put all three on a scatter plot with color by quality and drew and imaginary line to roughly split the ratings. Line added a clear divide, for increase in residual sugar and density being contained within the threshold set by the line, quality of the samples were observed to improve. While on the other hand, for the samples with increasing residual sugar level and density level above the line threshold, experts gave lower quality ratings.
Density and Fixed Acidity with Quality for Red wine: For red wine, fixed acidity and density showed the highest correlation. I used these two with quality to see if there was a trend. Imaginary line for reference was again drawn here and there was a trend observed. For increasing fixed acidity per sample, density above the line threshold got good reviews i.e. high quality rating and density values less than the threshold received average to poor reviews.
OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.
##
## Calls:
## m1: lm(formula = quality ~ alcohol, data = combined_wq)
## m2: lm(formula = quality ~ alcohol + pH, data = combined_wq)
## m3: lm(formula = quality ~ alcohol + pH + sulphates, data = combined_wq)
## m4: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5),
## data = combined_wq)
## m5: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide, data = combined_wq)
## m6: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)), data = combined_wq)
## m7: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity,
## data = combined_wq)
## m8: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid, data = combined_wq)
## m9: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)), data = combined_wq)
## m10: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)),
## data = combined_wq)
## m11: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)) +
## residual.sugar, data = combined_wq)
## m12: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)) +
## residual.sugar + I(log10(combined.acidity)), data = combined_wq)
## m13: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)) +
## residual.sugar + I(log10(combined.acidity)) + s.a.ratio,
## data = combined_wq)
## m14: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)) +
## residual.sugar + I(log10(combined.acidity)) + s.a.ratio +
## taste, data = combined_wq)
## m15: lm(formula = quality ~ alcohol + pH + sulphates + I(sulphates^5) +
## free.sulfur.dioxide + I(free.sulfur.dioxide^(1/10)) + volatile.acidity +
## citric.acid + I(log10(density)) + I(log10(total.sulfur.dioxide)) +
## residual.sugar + I(log10(combined.acidity)) + s.a.ratio +
## taste + fixed.acidity, data = combined_wq)
##
## ===================================================================================================================================================================================================================
## m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15
## -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 2.405*** 2.982*** 2.987*** 3.023*** 2.277*** -1.983*** -1.028** -0.927* -1.316** -2.164*** -2.466*** -4.232*** -4.160*** -4.748*** -3.973***
## (0.086) (0.204) (0.204) (0.204) (0.209) (0.396) (0.388) (0.401) (0.404) (0.407) (0.406) (0.574) (0.594) (0.605) (0.747)
## alcohol 0.325*** 0.328*** 0.329*** 0.329*** 0.348*** 0.342*** 0.323*** 0.323*** 0.381*** 0.352*** 0.303*** 0.261*** 0.261*** 0.246*** 0.238***
## (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.011) (0.012) (0.013) (0.016) (0.016) (0.017) (0.018)
## pH -0.189** -0.241*** -0.267*** -0.195** -0.187** 0.073 0.055 0.024 -0.044 0.101 0.360*** 0.359*** 0.402*** 0.417***
## (0.061) (0.062) (0.063) (0.062) (0.061) (0.061) (0.064) (0.063) (0.063) (0.065) (0.088) (0.088) (0.090) (0.090)
## sulphates 0.284*** 0.385*** 0.551*** 0.681*** 0.821*** 0.834*** 0.693*** 0.547*** 0.767*** 0.829*** 0.828*** 0.844*** 0.850***
## (0.066) (0.076) (0.076) (0.076) (0.074) (0.075) (0.077) (0.078) (0.082) (0.083) (0.083) (0.083) (0.083)
## I(sulphates^5) -0.038** -0.043** -0.052*** -0.050*** -0.051*** -0.043** -0.034** -0.040** -0.039** -0.039** -0.039** -0.038**
## (0.014) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) (0.013)
## free.sulfur.dioxide 0.007*** -0.009*** -0.009*** -0.008*** -0.009*** -0.013*** -0.014*** -0.014*** -0.014*** -0.015*** -0.015***
## (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
## I(free.sulfur.dioxide^(1/10)) 3.433*** 2.517*** 2.499*** 2.685*** 4.660*** 4.717*** 4.700*** 4.705*** 4.799*** 4.821***
## (0.272) (0.268) (0.269) (0.269) (0.319) (0.317) (0.317) (0.317) (0.316) (0.316)
## volatile.acidity -1.247*** -1.269*** -1.429*** -1.558*** -1.380*** -1.396*** -1.399*** -1.397*** -1.300***
## (0.063) (0.067) (0.071) (0.071) (0.074) (0.074) (0.074) (0.074) (0.092)
## citric.acid -0.070 -0.206** -0.131 0.013 -0.116 -0.118 -0.112 -0.045
## (0.072) (0.075) (0.074) (0.076) (0.081) (0.081) (0.081) (0.090)
## I(log10(density)) 78.845*** 60.937*** -44.217* -132.737*** -132.288*** -151.958*** -163.429***
## (11.236) (11.239) (17.213) (26.631) (26.649) (28.208) (28.938)
## I(log10(total.sulfur.dioxide)) -0.598*** -0.758*** -0.763*** -0.767*** -0.798*** -0.799***
## (0.053) (0.056) (0.056) (0.057) (0.057) (0.057)
## residual.sugar 0.028*** 0.043*** 0.050** 0.024 0.033
## (0.004) (0.005) (0.016) (0.017) (0.018)
## I(log10(combined.acidity)) 1.267*** 1.196*** 1.600*** -0.092
## (0.291) (0.326) (0.348) (1.017)
## s.a.ratio -0.057 0.322* 0.262
## (0.118) (0.132) (0.136)
## taste: .L 0.179 0.183
## (0.559) (0.559)
## taste: .Q 0.550 0.555
## (0.408) (0.407)
## taste: .C 0.365 0.367*
## (0.187) (0.187)
## fixed.acidity 0.089
## (0.050)
## -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## R-squared 0.197 0.199 0.201 0.202 0.223 0.242 0.284 0.285 0.290 0.304 0.311 0.313 0.313 0.318 0.318
## adj. R-squared 0.197 0.198 0.200 0.201 0.222 0.241 0.284 0.284 0.289 0.303 0.309 0.311 0.311 0.316 0.316
## sigma 0.782 0.782 0.781 0.780 0.770 0.761 0.739 0.739 0.736 0.729 0.726 0.725 0.725 0.722 0.722
## F 1597.641 804.749 544.025 410.377 372.584 344.582 368.568 322.613 294.371 282.976 265.644 245.759 226.845 188.468 177.624
## p 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7623.404 -7618.549 -7609.411 -7605.540 -7518.180 -7439.467 -7250.383 -7249.909 -7225.344 -7161.667 -7129.474 -7120.000 -7119.884 -7096.585 -7095.014
## Deviance 3975.734 3969.796 3958.645 3953.930 3849.017 3756.874 3544.442 3543.924 3517.226 3448.953 3414.943 3404.997 3404.876 3380.543 3378.909
## AIC 15252.809 15245.098 15228.821 15223.079 15050.360 14894.933 14518.766 14519.817 14472.687 14347.334 14284.948 14267.999 14269.768 14229.170 14228.028
## BIC 15273.146 15272.214 15262.717 15263.754 15097.814 14949.166 14579.778 14587.608 14547.257 14428.683 14373.076 14362.907 14371.454 14351.194 14356.831
## N 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497 6497
## ===================================================================================================================================================================================================================I created a model for predicting the quality of wine samples. The variables used in this model are combination of original plus the derived and log transformed variables. Although, the linear model only showed an r^2 of 0.32, I tried to put in as useful features I could. Feature selection was a combination of correlation coefficient calculations performed in the previous sections and trial & error used to check which combination (log or power multiples) gave better results.
Final Plots and Summary
Plot One
Description One
First plot is chosen from the univariate section. It shows the frequency polygons for the distribution of alcohol for White and Red wine samples. The frequency polygons show that for most of the samples for both wine types, alcohol percentage is between 9% and 13%. Apart from the difference in the number of samples, just by looking at the plot it seems that both wine types have same composition of alcohol with multiple peaks 9.5, 10.1, 10.5 and 11.1% for white wine and 9.5, 9.8, 10.5 and 10.9% for red wine samples. There seems to be a similarity in the shapes of the polygons too and reminds me of a geometric transformation with approximate enlargement factor of 2.
Plot Two
Description Two
Plot two is a combination of quality vs. alcohol box plots for both wine types, take from the bivariate section of this report. Stat summary function is used to plot mean value of alcohol for each quality rating bucket denoted by a green cross inside a box plot. For both wine types, mean and median alcohol levels for lower quality ratings (3-5) show a slight drop but as we progress through higher quality buckets there is an increasing trend seen in percentage of alcohol. There is no red wine sample that got quality rating of 9 from the experts.
Plot Three
Description Three
Third plot is derived from the multivariate section. Frequency polygon and box plot have already been discussed in the previous plots so I thought of including a scatter plot. Legend for quality is set in such a way that orangish tint corresponds towards lower quality rating and greenish tint towards higher quality rating and only quality rating buckets (5-7) with most samples are chosen. Considering only the quality buckets with most samples would help understand the trend. The data subset used for this plot also excludes outliers for both pH and sulphates. I have used a combination of facet wrap and grid arrange to show comparison between pH and sulphate.
White wine
For white wine, the scatter plots generally show that with increase of sulphate and alcohol content experts tend to give higher quality ratings to the samples. I can say the same for pH and Alcohol, increase in values of both these variables, improves quality rating. Let us look at the summary and r^2 values as part of this investigation.
Summary of Sulphate, pH and Alcohol content for White wine
pH
## sub_q_wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.790 3.080 3.160 3.169 3.240 3.790
## --------------------------------------------------------
## sub_q_wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.720 3.080 3.180 3.189 3.280 3.810
## --------------------------------------------------------
## sub_q_wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.840 3.100 3.200 3.214 3.320 3.820SO4
## sub_q_wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2700 0.4200 0.4700 0.4822 0.5300 0.8800
## --------------------------------------------------------
## sub_q_wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2300 0.4100 0.4800 0.4911 0.5500 1.0600
## --------------------------------------------------------
## sub_q_wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2200 0.4100 0.4800 0.5031 0.5800 1.0800Alcohol
## sub_q_wqw$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.000 9.200 9.500 9.809 10.300 13.600
## --------------------------------------------------------
## sub_q_wqw$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.50 9.60 10.50 10.58 11.40 14.00
## --------------------------------------------------------
## sub_q_wqw$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.60 10.60 11.40 11.37 12.30 14.20r2 table of Sulphate, pH and Alcohol content for White wine
## pH sulphates alcohol quality
## pH 1.00 0.15 0.12 0.10
## sulphates 0.15 1.00 -0.02 0.06
## alcohol 0.12 -0.02 1.00 0.45
## quality 0.10 0.06 0.45 1.00We can see that with increase in quality rating, mean and median values for pH, alcohol and sulphate content generally increase confirming the analysis done by looking at the scatter plots. Correlation table also shows a positively increasing relationship between quality and all the other 3 variables with alcohol being the strongest and SO4 being the weakest. Generally for the data set available and majority of the samples of White wine, increase in alcohol, pH and SO4 content improves quality.
Red wine
It can be observed from the plot that there is a slight positive correlation between SO4 and alcohol which in turn improves the quality ratings. On the other hand, samples with increase in pH and decrease in alcohol receive lower ratings while the ones with relatively low pH and higher alcohol content seem to receive higher quality ratings. Summary table and r^2 values are as follows for further investigation.
Summary of Sulphate, pH and Alcohol content for Red wine
pH
## sub_q_wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.880 3.200 3.300 3.305 3.400 3.740
## --------------------------------------------------------
## sub_q_wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.860 3.220 3.320 3.318 3.410 4.010
## --------------------------------------------------------
## sub_q_wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.920 3.200 3.280 3.291 3.380 3.780SO4
## sub_q_wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.370 0.530 0.580 0.621 0.660 1.980
## --------------------------------------------------------
## sub_q_wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4000 0.5800 0.6400 0.6753 0.7500 1.9500
## --------------------------------------------------------
## sub_q_wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3900 0.6500 0.7400 0.7413 0.8300 1.3600Alcohol
## sub_q_wqr$quality: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.5 9.4 9.7 9.9 10.2 14.9
## --------------------------------------------------------
## sub_q_wqr$quality: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.80 10.50 10.63 11.30 14.00
## --------------------------------------------------------
## sub_q_wqr$quality: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.20 10.80 11.50 11.47 12.10 14.00r2 table of Sulphate, pH and Alcohol content for Red wine
## pH sulphates alcohol quality
## pH 1.00 -0.18 0.2 -0.01
## sulphates -0.18 1.00 0.1 0.24
## alcohol 0.20 0.10 1.0 0.50
## quality -0.01 0.24 0.5 1.00Mean and median values for alcohol and sulphate content generally increase with improving quality ratings confirming what was observed in the scatter plots. In contrast to this, mean and median values for pH fluctuates with improving quality. The pH increases from quality rating of 5-6 and then decreases for quality rating 7. This fluctuation results in a negative correlation also confirmed by the r^2 value of -0.01. For majority of the Red wine samples, increase in alcohol and SO4 improves the quality rating as seen in the correlation table while pH has negligible effect on quality.
Reflection
Analysis and Obervations
The analysis of the two wine data sets kicked off with the selection of main features. As the main objective of the project was to determine the quality rating of a particular wine sample based on its chemical composition, ‘quality’ and a very close associated variable ‘alcohol’ were chosen to be the two main features. Main features held the center stage and analysis revolved around them. In addition to the main features, some of the other variables in the data sets were considered as supporting features.
In the univariate analysis section for the project, I had assumed that along with the main features, supporting features like residual sugar and acidic contents (fixed, volatile and citric acid) would play an important role in the analysis. I had also thought features like pH, density and sulphate content would be very useful in determining the quality of wine samples.
All feature selection was considered for both the wine types in general. Conducting extensive comparative analysis of the features in bivariate and multivariate sections revealed some interesting relationships and combinations that might affect the quality of wine samples.
The sequence of the analysis conducted and the successes/difficulties faced during the analysis of the two wine data sets is summarized below:
I started with analyzing the relationship between quality and alcohol. Correlation coefficient, regression line and the scatter plot showed positive relation between the two, however, the exact trend was difficult to pin point. I took an alternative approach and created box plots and showed mean alcohol levels for each quality bucket. The box plots and the mean values showed that although there was a positive correlation but it was not linear for all the buckets of quality. For both the wine type, alcohol content at lower quality ratings, showed degradation and then from quality rating of 5 onwards there was a positive linear trend observed.
Evidence of this observation is shown in the correlation coefficient calculation done below (I have not included this in an r chunk as this just for illustration purposes). Sub-setting by quality, both the wine types are compared for lower and upper buckets of quality ratings.
Comparison of r^2 for subsets for White wine
cor.test(alcohol, quality) = 0.44
with(subset(wqw, quality < 5), cor.test(alcohol, quality)) = -0.06
with(subset(wqw, quality > 4), cor.test(alcohol, quality)) = 0.47
Comparison of r^2 for subsets for Red wine
